I've been having the same problems on my S4 mini since the latest ios update. Except, I have no pictures, nu music and no videos. All downloaded apps are on the SD card except for Facebook (only because it can't be moved to the SD card)
I have 5gb free on the SD card,
but only 470mb internal space.
My downloaded files folder, which is empty, shows that it takes 94mb.
I tried to download the maid app, but I don't have enough space.
I don't know what I can uninstall without causing problems, since everything that is on the internal space thingy either came with the phone or with updates... So I'm pretty stuck.
I'd prefer not to restore to factory settings since I did that just a couple of months ago and some of my games reset and the settings in some of my programs just wouldn't work right, it was a lot of hassle.
I did try turning off document sync, and it changed absolutely nothing.
Any ideas?